Ultrasound method and apparatus

ABSTRACT

Embodiments described provide an ultrasound method, and an ultrasound apparatus and computer program product operable to perform that method. In some embodiments, the method allows for provision of a multi-transducer ultrasound imaging system by providing a robust method to accurately localize the transducers in the system in order to beamform a final image. The method and apparatus described allow for improvements in imaging quality in terms of resolution, depth penetration, contrast and signal to noise ratio (SNR).

FIELD OF THE INVENTION

Aspects and embodiments described provide an ultrasound method and anultrasound apparatus and computer program product operable to performthat method.

BACKGROUND

Ultrasound is a widely used analysis tool. Advantages of ultrasoundinclude safety and low cost compared to other possible analysis tools.However, conventional ultrasound systems can yield information which maybe difficult to assess, for example, as a result of limited resolutionand view-dependent artefacts that are inherent to ultrasound transducerstypically used. Ultrasound imaging using typical ultrasound transducerscan be particularly challenging, for example, if seeking to image atlarge depths.

SUMMARY

A first aspect provides an ultrasound method comprising: configuring twoor more separate ultrasound transmitters to transmit a signal into acoincident region; configuring a receiving array to receive wavefrontsrepresentative of a transmitted signal from each of the two or moretransmitters after interaction of the transmitted signal with a mediumlocated within the coincident region; analysing each of the receivedwavefronts to determine a relative spatial position of each of the twoor more separate ultrasound transmitters; and using the determinedrelative spatial position of each of the two or more separate ultrasoundtransmitters to perform coherent signal combination of the wavefrontsreceived at the receiving array from each of the two or moretransmitters after interaction of the transmitted signal with the mediumlocated within the coincident region.

Various mechanisms to improve data collected using ultrasound techniquesare known. Such mechanisms include, for example, compound datacollection methods and system arrangements, extended field of viewmethods and system arrangements and arrangements which operate toincrease an effective aperture of an ultrasound data collection system.

The first aspect recognises that a typical ultrasound transducer,comprising a transmitting array and a receiving array, is usuallydimensioned for a particular application. For example, in a clinical ormedical environment, a transducer is dimensioned to allow for anoperator to hold and move the transducer and the shape and size of thetransducer is such that it can maintain contact with the surface of ahuman or animal body as it is moved around the surface of that body.Other applications of ultrasound can have similar limitations regardingphysical dimensions of an ultrasound transmitter and/or receiver. As aresult of physical constraints, data which can be collected viaultrasound techniques may be subject to limitations. It is wellrecognised, for example, in optical and radio frequency systems, thatincreasing the effective aperture can improve an image created fromcollected data.

Creation of an extended aperture ultrasound system may be limited bycomplexity, expense and ultrasound transducers having large physicaldimensions to allow for a large aperture have a limited adaptability todifferent applications.

The first aspect recognises that it may be possible to implement amethod, using simple ultrasound components, which allows for one or moreof the challenges in ultrasound applications to be addressed. A methodaccording to the first aspect recognises that one of the challenges inan ultrasound system can be accurate and precise location oftransmitting and receiving elements in that system. The first aspectprovides a method for location of key elements in a system, based oninformation collected by the ultrasound system. In particular, ratherthan needing to know or maintain a particular physical positioning ofone or more elements forming an ultrasound system, the first aspectprovides a method to determine physical positioning by using ultrasoundwaves transmitted and received by elements of the system at the sametime that the elements are operating to collect information about amedium under study using ultrasound methods. A method according to thefirst aspect may provide a mechanism to both determine the position ofkey operational elements of an ultrasound system and, having determinedthose positions, interpretation of data collected by the ultrasoundsystem may be improved.

The first aspect provides an ultrasound method. That ultrasound methodmay comprise a medical or clinical ultrasound method. The ultrasoundmethod may comprise a medical ultrasound imaging method. The method maycomprise a step comprising: configuring two or more separate ultrasoundtransmitters to transmit a signal into a coincident region. Thosetransmitters may comprise a point transmitter or transmitting element ortransmitting array. The transmitting array may comprise a plurality oftransmitting elements. In either instance, the signal transmitted by thetwo or more ultrasound transmitters passes through an at least partlyoverlapping, or coincident region. That region may comprise an imagingregion, into which a medium to be studied may be placed.

The method of the first aspect may comprise a step of: configuring areceiving array to receive wavefronts representative of a transmittedsignal from each of the two or more transmitters after interaction ofthe transmitted signal with a medium located within the coincidentregion. The receiving array may comprise a plurality of receiverelements configured to receive the signals transmitted after they havebeen scattered by the medium under study. The method may comprise a stepof analysing each of the received wavefronts received by the receivingarray. That analysing of the form of the received wavefronts at thereceiving array can allow for determination of a relative spatialposition of each of the two or more separate ultrasound transmitters.Analysing each of the wavefronts received by the receiving array maycomprise analysing one or more wavefront received at the receiving arraybased on a signal transmitted by a first ultrasound transmitter andanalysing one or more wavefront received at the receiving array from asecond ultrasound transmitter. The wavefronts received from the firstand second ultrasound transmitters may be compared.

The method may then comprise using the determined relative spatialposition of each of the two or more separate ultrasound transmitters toperform coherent signal combination of the wavefronts received at thereceiving array from each of the two or more transmitters afterinteraction of the transmitted signal with the medium located within thecoincident region. Accordingly, by analysing received wavefronts over atemporal window to determine relative spatial position of the separateultrasound transmitters it becomes possible to perform a coherent signalcombination and therefore potentially obtain an improved image of amedium within the coincident region.

The method of the first embodiment may be performed with as few as two,effectively separate, ultrasound transmitters. The transmitters may bedistinct remote and/or physically separate. The receiving array may beco-located with a transmitter or may be remote from the transmitters.

The first aspect recognises that using the ultrasound signals themselvesto calculate the relative positions of the transmitters means that thereis no need to precisely know, for example, using translation stageequipment or similar, or restrain, the physical positions of ultrasoundtransmitters in space. The significant requirement is that the signalsfrom the transmitters, received at the receiving array, at least partlyoverlap in a region of interest. In other words, provided thetransmitters are directed towards an identical (overlapping) volume ofmedium of interest, it is possible to make use of the method of thefirst aspect and use the ultrasound signals received at the receivingarray to determine the positioning of the transmitters.

In one embodiment, the analysing comprises: selecting one or moreparameters defining the relative spatial position of each of the two ormore separate ultrasound transmitters. Accordingly, any set ofparameters which together act to define a location of the transmittersin space can be selected. In one embodiment, a selection of a set ofparameters is made, together with a set of possible ranges for eachparameter. An initial “seed” guess within the relevant range offeringrelative transmitter location may be used as a starting position forthen implementing an optimisation method in accordance with the firstaspect.

In one embodiment, the analysing comprises: using the receivedwavefronts to make an initial guess at one or more parameters definingthe relative spatial position of each of the two or more separateultrasound transmitters. That is to say, a coarse guess of relativetransmitter location can be made, that guess being made in dependenceupon received wavefronts. For example, wavefronts received from eachtransmitter from a scatterer within a medium may be identified. Sincethe difference in receive time between the two received wavefrontsscattered by the same scatterer will attributable to a difference intransmitter to common-scatterer transit time, an estimate of distancecan be made.

In one embodiment, the analysing comprises: receiving an indication ofone or more parameters defining the relative spatial position of each ofthe two or more separate ultrasound transmitters from one or moreorientation sensors provided at each ultrasound transmitter.Accordingly, an initial guess, which can be refined by means of anapproach in accordance with the first aspect, can be provided byphysical positioning sensor(s) provided. Those sensors may be located ona transmitter body, for example.

In one embodiment, the parameters comprise: a combination of one or moreparameters which allow the relative spatial position of each of the twoor more separate ultrasound transmitters to be determined. Accordingly,a combination of angle and distance and other similar parameters may beselected.

In one embodiment, the parameters comprise: one or more of: location ofone or more scatterer located within the medium located within thecoincident region; relative angle between the ultrasound transmitters;relative distance of the ultrasound transmitters from the receivingarray; speed of sound within the medium located within the coincidentregion. In one embodiment, the parameters consist of: location of one ormore scatterer located within the medium located within the coincidentregion; relative angle between the ultrasound transmitters; relativedistance of the ultrasound transmitters from the receiving array; speedof sound within the medium located within the coincident region orequivalents thereof.

In one embodiment, the analysing comprises: increasing correspondencebetween the received wavefronts by refining the parameters defining therelative spatial position of each of the two or more separate ultrasoundtransmitters. In one embodiment, the correspondence comprises: acorrelation between the received wavefronts. Accordingly, an iterativeprocess is used to perform the analysing step of a method of the firstaspect. Various criteria can be used to “stop” the iterative or refiningprocess. The stopping criteria may comprise a selected number ofiterations. The stopping criteria may comprise a measure of fit passinga selected threshold value. The stopping criteria may comprise a maximaor minima or rate of change of a fit parameter reaching a plateau.

In one embodiment, the method further comprises: using the refinedparameters to select the relative spatial position to be used whenperforming the coherent signal combination. Accordingly, once a refinedspatial position of the transmitters is calculated, then coherent signalcombination of the information received at the receiving array from eachtransmitter can be performed. That is to say, it is possible to matchreceived signals at the receiving array from the two or more ultrasoundtransmitters.

Some implementations of the first aspect may provide an ultrasoundmethod comprising: configuring two or more separate ultrasoundtransmitters to transmit a signal into a coincident region; configuringa receiving array to receive wavefronts representative of a transmittedsignal from each of the two or more transmitters after interaction ofthe transmitted signal with a medium located within the coincidentregion; analysing each of the received wavefronts to determine anindication of a relative spatial position of each of the two or moreseparate ultrasound transmitters; and using the determined indication ofrelative spatial position of each of the two or more separate ultrasoundtransmitters to calculate one or more properties of the medium locatedwithin the coincident region. In some embodiments, the one or moreproperties may comprise a speed of sound signal within (sub)areas of themedium. In some embodiments, the one or more properties may comprise adensity map of areas of the medium. It will be appreciated thatwavefront aberration caused by an inhomogeneous medium can limit thequality of ultrasound images and is one significant barrier to achievingdiffraction-limited resolution with large aperture transducers [18]. Oneimplementation of a method in accordance with the first aspect mayassume the speed of sound is constant along a propagation path. However,since the speed of sound is a parameter which may be optimised in someembodiments, the method described can be adapted to apply tonon-homogeneous media in which the speed of sound varies in space. Insuch a case, for example, the medium could be modelled by piecewisecontinuous layers. The optimization method could be applied in arecursive manner, dividing a FoV into appropriate sub areas withdifferent speeds of sound. More accurate speed of sound estimation mayallow for improved beamforming and allow for higher order phaseaberration correction. Furthermore, speed of sound maps within a mediumcan be of use in tissue characterization.

Implementations of the first aspect allow a system which avoids a needfor pre-calibration and/or prior knowledge of relative location of thetwo or more separate ultrasound transmitters arranged to transmit asignal into a coincident region. In particular, rather than needing toperform a direct transmission from transmitter to receiver in order tocalculate relative position of transmitter and receiver, it is possibleto use data obtained from a scattering medium under study to calculaterelative positions of the transmitters. Implementations using scattererswithin a medium under study to determine relative positioning of thetransmitters represent an efficient mechanism to ensure that thegeometry is always favourable (provided there is a coincident region).

Some implementations of the first aspect provide a method of usingshared information, for example, prominent scatterers or other prominentfeatures in received cross-transducer data to enable localisation ofapertures, even without the presence of clear point targets within amedium under study. In some arrangements, an exogeneous source ofprominent scatterers, for example, a low concentration of microbubbles,can be used to assist correlation between received cross-transducerdata. Implementations of the first aspect recognise that whilst typicalapertures (formed within each individual transmitter/receiver array) maybe subject to a maximum useable size set by the dispersion of the speedof sound within a medium under study, some embodiments may comprise a“super aperture” formed from multiple transmitter/receiver arrays andthe super aperture is not subject to that same maximum size constraint.’

A second aspect provides a computer program product operable, whenexecuted on a computer, to perform the ultrasound method of the firstaspect.

A third aspect provides ultrasound apparatus comprising: two or moreseparate ultrasound transmitters configured to transmit a signal into acoincident region; a receiving array configured to receive a wavefrontrepresentative of a transmitted signal from each of the two or moretransmitters after interaction of the transmitted signal with a mediumlocated within the coincident region; location processing logicconfigured to analyse each of the received wavefronts and determine arelative spatial position of each of the two or more separate ultrasoundtransmitters; and signal combination logic configured to use thedetermined relative spatial position of each of the two or more separateultrasound transmitters to perform coherent signal combination of thewavefronts received at the receiving array from each of the two or moretransmitters after interaction of the transmitted signal with the mediumlocated within the coincident region.

In one embodiment, the two or more separate ultrasound transmitters arelocated such that their signal volumes at least partly overlap withinthe coincident region. In other words, said two or more separateultrasound transmitters are located such that a field or cone of view ofeach of the separate ultrasound transmitters at least partly overlapswith a field of view of each other of the transmitters within saidcoincident region.

In one embodiment, the ultrasound signal comprises a pulsed ultrasoundsignal. The repetition rate of the ultrasound pulses can be dependentupon the depth within a medium of interest to be imaged. A higher pulsefrequency offers higher temporal sampling of a medium under study.

In one embodiment, the two or more separate ultrasound transmitters areconfigured to transmit a signal into the coincident region substantiallyconcurrently. In one embodiment, the two or more separate ultrasoundtransmitters are configured to transmit a signal into the coincidentregion consecutively. Depending upon application, an appropriatetransmission mode may be selected. Concurrent transmissions may increasecomputational complexity yet allow for increased sensitivity in theinformation collected by a receiving array.

In one embodiment, the signal transmitted by each of the two or moretransmitters comprises a plane wave. In one embodiment, the signaltransmitted by each of the two or more transmitters comprises a pointultrasound source. In one embodiment, the transmitted signal comprises aknown wave configuration. The transmitted signal may comprise anyreasonable known wave configuration, for example, a sine wave, orsimilar.

In one embodiment, the apparatus further comprises: at least one furtherreceiving array configured to receive the wavefront representative of atransmitted signal from each of the two or more transmitters afterinteraction of the transmitted signal with the medium located within thecoincident region; and wherein the location processing logic isconfigured to analyse each of the received wavefronts received at eachreceiving array and determine a relative spatial position of each of thetwo or more separate ultrasound transmitters; and wherein the signalcombination logic is configured to use the determined relative spatialposition of each of the two or more separate ultrasound transmittersfrom each receiving array to perform coherent image reconstruction ofthe medium located within the coincident imaging region by combiningwavefronts received at each the receiving array from each of the two ormore transmitters after interaction of the transmitted signal with amedium located within the coincident region. Accordingly, it may bepossible to perform the same analysis using two or more receivingarrays, thus effectively increasing the receive aperture.

In one embodiment, at least one of the two or more separate ultrasoundtransmitters and one or more of the receiving arrays are co-located toform an ultrasound transducer. In one embodiment, each of the two ormore separate ultrasound transmitters and receiving arrays areco-located to form an ultrasound transducer.

Further particular and preferred aspects are set out in the accompanyingindependent and dependent claims. Features of the dependent claims maybe combined with features of the independent claims as appropriate, andin combinations other than those explicitly set out in the claims. Inparticular, features of the first aspect may be incorporatedappropriately into the third aspect and vice versa.

Where an apparatus feature is described as being operable to provide afunction, it will be appreciated that this includes an apparatus featurewhich provides that function, or which is adapted or configured toprovide that function.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described further, withreference to the accompanying drawings, in which:

FIG. 1 is a geometric representation of a multi-transducer beamformingscheme;

FIG. 2 illustrates schematically an experimental setup comprising twoultrasound transducers;

FIG. 3 illustrates the experimental setup of FIG. 2 in more detail;

FIG. 4 shows graphically coherent multi-transducer images obtained usinginitial estimates of parameters and optimum values, the datacorresponding to that shown in Table I;

FIG. 5 is a box-plot of a normalized value of optimal parameters whichdefine a rigid-body transformation between coordinate systems and thespeed of sound over the duration of an experiment;

FIG. 6 shows images of a wire phantom obtained using a single transducerincoherently combined collected data and coherently combined collecteddata from two ultrasound transducers;

FIGS. 7 and 8 show a corresponding transverse cut of PSF at a scattererdepth indicated by FIG. 6;

FIG. 9 shows a comparison of envelope-detected PSFs and k-spacerepresentation obtained using a single transducer and a coherentmulti-transducer;

FIG. 10 illustrates envelope-detected PSFs and k-space representationsof a multitransducer ultrasound method, compounding 121 plane wavescovering a total angle range of 60°, without and with apodization;

FIG. 11 shows a set of individual sub-images forming a final “multicoherent” image;

FIG. 12 shows experimental images of a contrast phantom obtained bydifferent methods;

FIG. 13 is a schematic representation of a common field of view (FoV) oftwo probes T1 and T2;

FIG. 14 illustrates an example of a speed of sound map of a propagationmedium with a muscle layer of 8 mm thickness and a fat layer of 25 mm;

FIG. 15 is a schematic representation of spatial location of two lineararrays;

FIG. 16 is a schematic representation of spatial location of two lineararrays and their field of view at different imaging depths;

FIG. 17 is a conventional aperture image;

FIG. 18 illustrates a simulated PSF and lesion image from anon-aberrating medium for increasing effective aperture and gap of aCMTUS system;

FIG. 19 compares computed image quality metrics of a CMTUS approach witha 1 probe system;

FIG. 20 compares CMTUS images with the 1-probe system at two differentimaging depths (100 mm and 155 mm);

FIG. 21 compares computed quality metrics as a function of imagingdepth;

FIG. 22 is a comparison of simulated images acquired by a conventionalaperture 1-probe (a-d), 2-probes (e-h) and CMTUS method (i-l) throughaberrating layers of increasing thickness;

FIG. 23 shows simulated delayed RF data for a medium with a fat layer of35 mm thickness;

FIG. 24 is a comparison of computed quality metrics across differentimaging methods;

FIG. 25 shows a comparison of the phantom images acquired with 1-probeand CMTUS in the control case and through a paraffin wax sample;

FIG. 26 shows a comparison of computed quality metrics, lateralresolution (LR), contrast and contrast-to-noise-ratio (CNR),experimentally measured for two different acquisition techniques;

FIG. 27 compares experimental point target images; and

FIG. 28 shows experimental delayed RF data obtained using differentbeamforming parameters.

DESCRIPTION OF THE EMBODIMENTS

Before describing one particular embodiment in detail, a generaloverview of methods and devices utilising concepts described isprovided.

It is recognised throughout imaging systems that an extended aperturehas potential to improve imaging performance [1]. When using ultrasoundas an analysis tool, particularly in a clinical context, aperture sizecan be limited by complexity and expense associated with an extendedaperture system. Furthermore, ultrasound transducers having largephysical dimensions to allow for a large aperture have a limitedadaptability to different applications.

Taking as one example, clinical use of ultrasound for imaging, typicalclinical ultrasound probes are controlled and moved by a physician toadapt to contours and shapes of a human body. Physical ultrasoundtransducer size becomes a compromise between cost, ergonomics and imageperformance. Providing a method by which ultrasound image quality may beimproved without altering dimensions of conventional ultrasound probesmay be useful.

Improvements associated with a wider coherent aperture have been shownin synthetic aperture ultrasound imaging [2], [3]. In thosearrangements, an extended aperture is obtained by mechanically movingand tracking an ultrasound transducer. Detailed position and orientationtracking information is used to identify a relative position andorientation of obtained ultrasound images which are then merged togetherinto a final image [4]. However, tracking system noise and calibrationerrors propagate to coherent image reconstruction, causing imagedegradation. In practical terms, subwavelength localization accuracy isrequired to merge information from multiple poses. Such accuracy ischallenging to achieve in conventional ultrasound calibration. For apractical implementation, a more accurate calibration technique isrequired [3], [5]. In addition, viability of the technique in-vivo islimited by long acquisition times (>15 minutes per image) which maybreak down a coherent aperture [6]. Resolution suffers from motionartefacts, tissue deformation and tissue aberration, all of which worsenwith increased effective aperture size [7].

Methods according to some aspects and embodiments may provide a fullycoherent multi-transducer ultrasound imaging system. That system can beformed from a plurality of ultrasound transducers which aresynchronized, freely disposed in space and configured to transmit planewaves (PW). By coherently integrating different transducers a largereffective aperture, in both transmit and receive, can obtained and animproved final image can be formed. As described previously, coherentcombination of information obtained by the different transducersrequires the position of transmitters and receivers within the system tobe known to subwavelength accuracy.

In general, a method is described which can achieve an accuratesubwavelength localization of ultrasound transmitters (and receivers)within a multi-transmitter system. Based on a spatial coherence functionof backscattered echoes originating from a common point source receivedby the same transducer; multiple transducers of a multi-transducerultrasound imaging system can be localized without use of an externaltracking device. Using plane waves (PW) generates a higher energywavefield than in a synthetic aperture approach, therefore improvingpenetration. Use of PW also enables higher frame rates [8].

The principles of classic PW imaging are summarized below together withnomenclature used and an overview of multiple transducer beamforming. Amethod to accurately calculate the spatial location of the differenttransducers is described. Experimental phantom measurements aredescribed and corresponding results, obtained using a multi-transducersystem, are shown. Results are compared to conventional PW imaging usinga single transducer and incoherently compounded images from theplurality of transducers.

Theory

Ultrasound image quality improves by reducing the F number, whichrepresents a ratio of focusing depth to an aperture size. Expanding anaperture is a direct wayto improve imaging performance. Hence, ifinformation from different transducers can be coherently combined,significantly increasing aperture size of a system, an enhanced image isexpected.

In one possible coherent multi-transducer method, a single transducer isused for each transmission to produce a plane wave (PW) that isolates anentire Field of View (FoV) of the transmit transducer. Resulting echoesscattered from a medium are recorded using all transducers forming partof the multi-transducer system. A data collection sequence is performedby transmitting from each individual transducer in turn. Knowing thelocation of each transducer (and taking into account full transmit andreceive path lengths) coherent summation of collected data from multipletransducers can be used to form a larger aperture and obtain image,following a conventional PW imaging approach.

Multi-Transducer Notation and Beamforming

A 3-D framework consisting of N matrix arrays, freely disposed in space,having a partly shared field of view (FoV) is considered. Such aframework represents positioning of a plurality of ultrasoundtransducers. Other than an at least partly overlapping field of view,the transducers can be considered to be otherwise at arbitrary positionsin space. The transducers are synchronized (in other words, in thisarrangement, trigger and sampling times in both transmit and receivemode of the ultrasound transducers are the same). The ultrasoundtransducers are configured to take turns to transmit a plane wave into amedium. The arrangement is such that each transmitted wave is receivedby all transducers, including the transmitting one. Thus, a single planewave shot yields N RF datasets—one associated with each receivingtransducer.

The framework is described using the following nomenclature:

Points are noted in upper case letters (e.g. P);

Vectors representing relative positions are represented in boldlowercase (e.g. r);

Unit vectors are noted with a “hat”; and

Matrices are written in bold uppercase (e.g. R).

Index convention is to use i for the transmitting transducer, j for thereceiving transducer, h for transducer elements, and k for scatterers.Other indices are described when used.

The set-up be defined by N matrix array transducers T_(i), i=1 . . . N,with H elements as illustrated in FIG. 1. The position and orientationof T_(i) is represented by the axes {x_(i), y_(i), z_(i)} and the originO_(i) defined at the centre of the transducer surface with the z₁direction orthogonal to the transducer surface and directed away fromtransducer 1. A plane wave transmitted by transducer T_(i) is defined bythe plane P_(i), which can be characterized through the normal to theplane n_(i) and the origin O_(i). The RF data received by transducer jon element h at time t is noted T_(i)R_(j)(h; t). The resulting imageand all transducer coordinates are defined in a world coordinate systemarbitrarily located in space, unless specifically referred to atransducer's local coordinate system in which case the superscript i isused.

FIG. 1 is a geometric representation of a multi-transducer beamformingscheme. In the example shown in FIG. 1, transducer T₁ transmits a planewave and T₂ receives the echo scattered from Q_(k) on element h. Usingthe notation set out above, plane wave imaging beamforming [8] can beextended to the multi-transducer scheme shown in FIG. 1. Assuming thattransducer Ti transmits a plane wave, the image point to be beamformedlocated at Q_(k) can be computed from the echoes received at transducerT_(j) as:

$\begin{matrix}{{s_{i,j}\left( Q_{k} \right)} = {{\sum\limits_{h = 1}^{H}{T_{i}{R_{j}\left( {h,{t_{i,h,j}\left( Q_{k} \right)}} \right)}}} = {\sum\limits_{h = 1}^{H}{T_{i}{R_{j}\left( {h,\frac{D_{i,h,j}\left( Q_{k} \right)}{c}} \right)}}}}} & (1)\end{matrix}$

where c is the speed of sound of the medium, and D is the distancetravelled by the wave, which can be split into the transmit and thereceive distances:

D _(i,h,j)(Q _(k))=d _(T)(Q _(k),

_(i))+d _(R|h)(Q _(k) ,O _(j) +r _(h))  (2)

with d_(T) measuring the distance between a point and a plane (transmitdistance), and d_(R;h) being the distance between a point and thereceive element (receive distance). These distances can be computed asfollows:

d _(T)(Q _(k),

_(i))=|(O _(i) −Q| _(k))•{circumflex over (n)}| _(i)  (3)

and

d _(R,h)(Q _(k) ,O _(j) +r _(h))|=∥Q _(k)−(O| _(j) +r _(h))∥=∥Q _(k)−(O_(j) +R _(j) r _(h) ^(j))∥  (4)

where ∥∥ is the usual Euclidean distance, and Rj=[x_(j)y_(j)z_(j)] is a3×3 matrix parameterized through three rotation angles:

ϕ_(j)={ϕ_(x),ϕ_(y),ϕ_(z)}_(j)

that together with the offset O_(j) characterize the position andorientation of transducer T_(j) with 6 parameters [9].

With the total distances computed, equation (1) can be evaluated foreach pair of transmit-receive transducers, and the total beamformedimage S(Q_(k)) can be obtained by coherently adding the individuallybeamformed images:

$\begin{matrix}{{S\left( Q_{k} \right)} = {\sum\limits_{i = 1}^{N}{\sum\limits_{j = 1}^{N}{s_{i,j}\left( Q_{k} \right)}}}} & (5)\end{matrix}$

Calculation of the Transducer Locations

In order to carry out the coherent multi-transducer compoundingdescribed above, the position and orientation of each imaging transduceris required. This then allows for computation of travel time of atransmitted wave to any receiving transducer. This section describes onemethod to accurately calculate those positions by exploiting consistencyof received RF data when transducers receive simultaneously from thesame transmitted (and scattered) wave. The method described assumes themedium is substantially homogeneous except for K point scattererslocated at positions Q_(k), k=1 . . . K, and all transducers areconsidered identical.

The following transmit sequence is considered:

a plane wave is transmitted by transducer T_(j) and received by Ntransducers forming the multi-transducer system;

a plane wave is transmitted by T_(j) and also received by alltransducers;

the process continues until the N transducers have transmitted in turn.

During the time during which each transmitter operates in turn, it isassumed that the system and medium under study remain perfectly still.

The wavefield resulting from the same scatterer and received by the sametransducer T_(j), when transmitting with all transducers, must becorrelated or have spatial covariance [10]. That is to say, for eachelement h, the only difference in timing is the transmit time (receivetime is equal since the receiving transducer is the same). The receivedsignals at the element h will be time correlated when the difference intransmit time is compensated for.

One method comprises finding the “optimal” parameters for which the timecorrelation between received RF datasets sharing a receive transducer isat a maximum for all scatterers in the common FoV.

Since the reception time depends also on the speed of sound in themedium c and on the position of the scatterers Q_(k), the unknownparameters are:

θ={c,Q ₁ , . . . ,Q _(K),ϕ₁ ,O ₁, . . . ,ϕ|_(N) ,O _(N)}  (6)

Note that, since the parameters that define transducer locations inspace depend on the definition of the world coordinate system, thevector of unknown parameters can be reduced by defining the worldcoordinate system the same as the local coordinate system of onetransducer.

The similarity between signals received by the same element can becomputed using the normalized crossed correlation NCC,

$\begin{matrix}{{{NCC}\left( {{y_{i,h,j,k}(\tau)},{y_{j,h,j,k}(\tau)}} \right)}==\frac{\sum\limits_{\tau = 0}^{T}{\left( {{y_{i,h,j,k}(\tau)} - {{\overset{\_}{y}}_{i,h,j,k}(\tau)}} \right)\left( {{y_{j,h,j,k}(\tau)} - {{\overset{\_}{y}}_{j,k,j,k}(\tau)}} \right)}}{\left\lbrack {\sum\limits_{\tau = 0}^{T}{\left( {{y_{i,h,j,k}(\tau)} \sim {{\overset{\_}{y}}_{i,h,j,k}(\tau)}} \right)^{2}{\sum\limits_{\tau = 0}^{T}\left( {{y_{j,h,j,k}(\tau)} - {{\overset{\_}{y}}_{j,h,j,k}(\tau)}} \right)^{2}}}} \right\rbrack^{1/2}}} & (7)\end{matrix}$

where y_(i;h;j;k) represents the signal backscattered from Q_(k) andreceived by element h on transducer j when transmitting from T_(i), andcan be calculated as:

y _(i,h,j)|_(k)(τ;θ)=T _(i) R _(j)(h,τ+t _(i,h,j)(Q _(k);θ)) withτ∈[0,T]  (8)

being T the time transmit pulse length.

Then, the total similarity, χ_(j,k); between RF data received by thesame transducer j can be calculated taking into account all the elementsas:

$\begin{matrix}{{\chi_{j,k}(\theta)} = {\sum\limits_{i}^{N}{\sum\limits_{h}^{H}{{{NCC}\left( {{G_{i,h,j,k}\left( {\tau;\theta} \right)},{G_{j,h,j,k}\left( {\tau;\theta} \right)}} \right)}{W_{i,h,j,k}(\theta)}{W_{j,h,j,k}(\theta)}}}}} & (9)\end{matrix}$

where

G_(i,h,j,k)=√{square root over (y_(i,h,j,k) ²+

{yi,h,j,k}²)} is the envelope of the signal

yi,h,j,k is the Hilbert transform;and W_(i,h,j,k) is defined as:

$\begin{matrix}{{{W_{i,h,j,k}(\theta)} = {\frac{1}{2} + {\frac{1}{2H}{\sum\limits_{h_{b} \neq h}^{H}{{{NCC}\left( {{y_{i,h,j,k}\left( {\tau;\theta} \right)},{y_{i,h_{b,j,k}}\left( {\tau;\theta} \right)}} \right)}\mspace{14mu}{with}\mspace{14mu} h}}}}},{h_{b} \in \left\lbrack {1,\ldots\mspace{14mu},H} \right\rbrack}} & (10)\end{matrix}$

The function W_(i,h,j,k) is an element-wise weight that represents howwell each element correlates with the rest of the elements in the sametransducer j.

If intra-transducer channel correlation is not considered, the undesiredscenario where the wave receive times are erroneous but in a similarmanner for different transmitting transducers could yield to a lowdissimilarity value for the wrong parameters.

Summing over all receiving transducers and scatterers yields a finalcost function to be maximized:

$\begin{matrix}{{\chi(\theta)} = {\sum\limits_{j}^{N}{\sum\limits_{k}^{K}{\chi_{j,k}(\theta)}}}} & (11)\end{matrix}$

The “optimal” parameters θ, which include: relative position andorientation of all transducers involved, the speed of sound in themedium, and the position of the scatterers within the medium, can befound by applying a search algorithm that maximizes the cost functionalχ′:

$\begin{matrix}{\overset{\_}{\theta} = {\arg\;{\max\limits_{\theta}{\chi(\theta)}}}} & (12)\end{matrix}$

Equation (12) can be maximized by using gradient-based optimizationmethods [11].

Methods

FIG. 2 illustrates schematically an experimental setup comprising twoultrasound transducers. The method was tested experimentally using 2identical linear arrays having a partly shared field of view (FoV) of anultrasound phantom. The identical linear arrays were located on the sameplane (y=0). In such a 2-D framework, the parameters that define theposition and orientation of the transducers are reduced to one rotationangle and one 2-D translation [9].

The experimental sequence starts with transducer 1 transmitting a planewave into the region of interest, in which 5 scatterers are located inthe common FOV of transducers 1 and 2.

The backscattered ultrasound field is received by both transducers inthe system (T₁R₁ and T₁R₂). Under the same conditions, the sequence isrepeated, transmitting with transducer 2 and acquiring the backscatteredechoes with both transducers, T₂R₁ and T₂R₂.

Phantom

Acquisitions were performed on a custom-made wire target phantom (200•mdiameter) submersed in distilled water. The phantom was positionedwithin the overlapping imaging region of the transducers, so that allscatterers were in the common FoV.

Experimental Setup The experimental setup comprises two synchronized256-channel Ultrasound Advanced Open Platform (ULA-OP 256) systems (MSDLab, University of Florence, Italy) [12]. Each ULA-OP 256 system wasused to drive an ultrasonic linear array made of 144 piezoelectricelements with a 6 dB bandwidth ranging from 2 MHz to 7.5 MHz (imagingtransducer LA332, Esaote, Firenze, Italy). Before acquisition, probeswere carefully aligned to be located in the same elevational plane usinga precise optomechanical setup. Each probe was held by a 3-D printedshell structure connected to a double-tilt and rotation stage and thenmounted on a xyz translation and rotation stage (Thorlabs, USA). Theimaging plane of both transducers (y=0) was that defined by two parallelwires immersed in the water tank.

FIG. 3 illustrates the experimental setup of FIG. 2 in more detail.Components shown in FIG. 3 are labelled with letters: (A) Linear array.(B) 3-D printed probe holder. (C) Double-tilt and rotation stage. (D)Rotation stage. (E) xyz translation stage.

Pulse Sequencing and Experimental Protocol

Two independent experiments were carried out. First, a stationaryacquisition in which both probes were mounted and fixed in theoptomechanical setup described above. The second experiment consisted ofa free-hand demonstration. In this case, both probes were held andcontrolled by an operator. The transducer movements were carefullyrestricted to the same elevational plane, i.e. y=0 and to keep twocommon targets in the shared FoV.

Two different types of pulse sequences were used.

During the stationary experiment, for each probe and at alternatingsequence, i.e. only one transducer transmits at each time while bothprobes receive, 121 plane waves, covering a total sector angle of 60°(from −30° to 30°, 0.5° step), were transmitted from the 144 elements ofeach probe at 3 MHz with a pulse repetition frequency equal to 4000 Hz.The total sector angle between transmitted plane waves was chosenapproximately the same as the angle defined between the probes. RF rawdata scattered up to 77 mm deep were acquired at a sampling frequency of39 MHz. No apodization was applied either on transmission or reception.The total time for this sequence was 60.5 ms.

During the free-hand demonstration, 21 plane angles (from −5° to 5°,0-5° step) were transmitted from each probe and RF raw databackscattered up to 55 mm deep were acquired. The remaining settingswere identical to the fixed probe experiment. The total acquired timeusing this sequence was 1 s.

Data Processing

An initial estimate of parameters

θ₀ ={c,Q ₁ , . . . ,Q _(K),ϕ₁ ,O ₁,ϕ₂ ,O ₂}

needed to start the optimization algorithm was chosen as follows:

The speed of sound of the propagation medium was chosen according to theliterature, in the case of water this is c=1496 m/s [13].

Considering the world coordinate system to be the same as the localcoordinate system of transducer 1 (ϕ₁=0, O₁=[0,0]) the parameters {ϕ₂,O₂} that define the position of transducer 2 were calculated by usingpoint-based image registration [14].

For the scatterer positions Q_(k), their initial value was calculatedusing a best-fit one-way geometric delay for the echoes returning fromthe targets, as described in [15].

Optimization was done using all the targets within the shared FoV.

For the stationary experiment, since there was no motion, only one setof optimal parameters is needed and all RF data corresponding to planewaves transmitted at different angles can be beamformed using the sameoptimal parameters. However, to validate the optimization algorithm, 121optimal parameter sets were calculated, one per transmit angle.

For the free-hand demonstration, each frame was generated using adifferent set of optimal parameters, where each subsequent optimizationwas initialized with the optimum value of the previous frame. Theproposed method was compared with the conventional B-mode imaging usingone single transducer and with the incoherent compounding of the B-modeimages acquired by two independent transducers. The images acquiredduring the stationary experiment were used for this image performanceanalysis. A final image was obtained using equation (5), by coherentlyadding the totality of the individual images acquired in one sequence(T₁R₁, T₁R₂, T₂R₁, T₂R₂):

S(Q _(k))=s _(1,1)(Q _(k))+s _(1,2)(Q _(k))+s _(2,1)(Q _(k))+s _(2,2)(Q_(k))  (13)

Spatial resolution was calculated from the point spread function (PSF)on a single scatterer. An axial-lateral plane for 2-D PSF analysis waschosen by finding the location of the peak value in the elevationdimension from the envelope detected data. Lateral and axial PSFprofiles were taken from the centre of the point target. The lateralresolution was then assessed by measuring the width of the PSF at the −6dB level and the axial resolution as the dimension of the PSF at the −6dB level in the axial (depth) direction.

In addition, the performance of the proposed multitransducer system, interms of image quality such a resolution, was described using afrequency domain or k-space representation. Axial-lateral RF PSFs wereextracted from the beamformed data and the k-space representation wascalculated using a 2-D Fourier transform. While the axial resolution isdetermined by the transmitted pulse length and the transmit aperturefunction, the lateral response of the system can be predicted by theconvolution of the transmit and receive aperture functions [16].

Results

The 121 optimal parameter sets calculated for each of the transmitangles in the stationary experiment converged to the same results. Theinitial and optimal values obtained are summarized in Table I below.

TABLE I INITIAL ESTIMATE AND OPTIMUM VALUES OF THE SYSTEM PARAMETERSParameter Initial value Optimum value c 1496 m/s 1450.4 m/s Q₁  [8.54,28.48] mm  [8.66, 28.16] mm Q₂  [3.78, 37.31] mm  [3.84, 36.87] mm Q₃ [−1.10, 45.05] mm [−1.15, 45.41] mm Q₄  [−6.00, 54.07] mm [−6.03,53.94] mm Q₅ [−10.68, 62.00] mm [−10.67, 62.12] mm  ϕ₂ 55.33° 56.73° O₂ [39.55, 22.83] mm [38.80, 23.06] mm

FIG. 4 shows graphically coherent multi-transducer images obtained usinginitial estimates of parameters and optimum values, the datacorresponding to that shown in Table I. It can be seen that a blurringeffect on a PSF in an image obtained using initial estimates ofpositional parameters may be compensated after optimization methods areimplemented.

The convergence illustrated in Table I and in FIG. 4 is also validatedby results originating from the free-hand experiment. In this case, eachtransmit angle was optimized over total acquisition time. Aftercalculating an initial estimate of positional parameters of a firsttransmitted PW, each subsequent optimization was initialized with theoptimum value of the previous transmission event.

FIG. 5 is a box-plot of a normalized value of optimal parameters whichdefine a rigid-body transformation between coordinate systems and thespeed of sound over the duration of the experiment. As could bepredicted, rotation and translation parameters present the higher valuerange, whilst the speed of sound in the medium can be consideredsubstantially constant. The averaged value of the optimal speed of soundover the acquisition time was 1466.00 m/s and the standard deviation0.66 m/s.

FIG. 6 shows images of a wire phantom obtained using a single transducer(T₁R₁) incoherently combined collected data (envelope detected imagesT₁R₁, T₂R₂) and coherently combined collected data (T₁R₁, T₁R₂, T₂R₁,T₂R₂) from two ultrasound transducers.

Comparison of the resulting images from a single transducer and thosefrom a multitransducer method, it can be seen that the reconstructedimages of the wire targets were clearly improved.

The PSFs of the three images can be compared. FIGS. 7 and 8 show acorresponding transverse cut of PSF at a scatterer depth indicated byFIG. 6 for each of the images, using a single PW at 0° and compounding121 PW over a total angle range of 60°, respectively.

To analyse the multi-transducer method, a world coordinate system thatleads to the best resolution and more conventional PSF shape is used.This coordinate system is defined by rotating the local coordinatesystem of transducer T₁ by the bisector angle between the twotransducers. In this coordinate system, the best possible resolution isaligned with the x-axis. The incoherent multitransducer results showbenefit from the optimization, since the optimum parameters were used toincoherently compound enveloped-detected sub-images T₁R₁ and T₂R₂. Theeffect of apodization in the multi-coherent PSF, accentuating the lowlateral frequencies, was analysed in the PSF generated compounding 121PW over a total angle range of 60°. The performance of all them issummarized in Table II.

TABLE II IMAGING PERFORMANCE FOR THE DIFFERENT METHODS. Axial Lateral1^(st) 2^(nd) resolution resolution sidelobe sidelobe [mm] [mm] [dB][dB] PW Conventional 0.9445 0.6674 −14.96 −20.79 Multi Incoherent 0.94740.7837 −20.87 — Multi Coherent 0.8109 0.1817 −11.46 −7.01 PWConventional 0.9002 0.6546 −20.22 — (121 angles) Multi Coherent 0.82460.1911 −9.94 −9.64 w/o (121 angles) Multi Coherent w/ 0.8391 0.2278−20.73 −9.45 (121 angles)

It can be seen that the coherent multi-transducer acquisition results inbest lateral resolution, and worst lateral resolution corresponds to anincoherent image generated by combining the independent images acquiredby both transducers.

Large differences are observed in the behaviour of the side lobes, whichare higher in the coherent multi-transducer method. When a single PW isused, the biggest difference is between the second side lobes, beingraised by 13 dB for the coherent multi-transducer method compared to theconventional single transducer method, while difference of the firstside lobes is 3.5 dB. This suggests that whilst significant imageimprovements can be achieved, the image may suffer from the effects ofside lobes. Apodization results in a significant reduction of the firstside lobe and resolution improvement of 65% compared to a conventionalimage acquired by a single transducer.

FIG. 9 shows a comparison of envelope-detected PSFs and k-spacerepresentation obtained using a single transducer and a coherentmulti-transducer. The PSFs obtained using a single transducer (T₁R₁) andcoherently compounding the images acquired by both transducers wereanalysed in the k-space representation. FIG. 9 shows the correspondingresults using a single PW at 0°. Images are represented in the localcoordinate system of transducer 1. An important consequence of thelinear system is that the superposition principle can be applied. Asexpected, the total k-space representation shows an extended lateralregion which corresponds to the sum of the four individual k spaces thatform an image in the coherent multi-transducer method.

It will be appreciated that since both transducers are identical buthave different spatial locations, they exhibit the same k-space response(identical transmit and receive aperture functions) but in differentspatial locations. The discontinuity in the aperture of the system,given by the separation between the transducers, leads to gaps in thespatial frequency space. The discontinuity can be filled compounding PWover an angle range similar to the angle defined by the two transducers.

FIG. 10 illustrates envelope-detected PSFs and k-space representationsof a multitransducer ultrasound method, compounding 121 plane wavescovering a total angle range of 60°, without and with apodization. Inparticular, FIG. 10 shows the resulting PSF after compounding 121 angleswith a separation of 0.5°, which define a total sector of 60°, and thecorresponding continuous k-space. The topography of the continuousk-space can be re-shaped by weighting data from the different imageswhich are combined to form a final image. A more conventional transferfunction, displaying reduced side lobes can be created accentuating thelow lateral spatial frequencies, which are mostly defined by thesub-images T₁R₂ and T₂R₁. FIG. 10 shows a PSF and its correspondingk-space representation generated weighting the sub-images T₁R₁, T₁R₂,T₂R₁ and T₂R₂ with the vector [1; 2; 2; 1].

DISCUSSION

The study described introduces a new synchronized multi-transducerultrasound system and method which is capable of significantlyoutperforming conventional PW ultrasound imaging by coherently addingall individual images acquired by different transducers. In addition toan extended FoV that the use of multiple transducers allows for,improvements in resolution have been experimentally shown.

Furthermore, a final image formed from a coherent combination ofsub-images may present different characteristics to those shown in theindividual images. For example, a final image may have areas withoptimal performance in a common FoV of multiple transducers, and itsquality may deteriorate outside this region where the number oftransducers with a shared FoV decreases. The worst regions of a finalimage will typically be defined by the performance of individual imagesand correspond to the parts of the combined “final” image with nooverlapping FoV.

Different transmit beam profiles (such diverging waves) may increase theoverlapped FoV and extend the high-resolution areas of a final image.

The significant differences between the k-space representations for thesingle and the multi-transducer methods shown in the Figures furtherexplain differences in imaging performance. The more extended k-spacerepresentation, the higher resolution [17].

The appearance of the total response of a multi-transducer system can beexplained using the rotation and translation properties of the 2-DFourier transform. This total extent determines the highest spatialfrequencies present in the image and therefore dictates resolution. Therelative amplitudes of the spatial frequencies present, i.e. thetopography of k-space, determine the texture of imaged targets.Weighting the data from the different transducers can reshape thek-space, accentuating certain spatial frequencies and allow for creationof a more conventional response of a system.

The presence of uniformly spaced unfilled areas in a system's k-spaceresponse may indicate the presence of grating lobes in the system'sspatial impulse response [16]. A sparse array (such as thetwo-transducer system described above) creates gaps in k-space response.If a k-space has negligible gaps, the k-space magnitude response becomessmooth and continuous over a finite region. This is motivation to findand use a good spatial distribution for transducers in a system andsuggests that while it may be beneficial to compound PW at differentangles, it may not always be necessary in order to produce an improvedimage.

Wavefront aberration caused by an inhomogeneous medium can limit thequality of ultrasound images and is one significant barrier to achievingdiffraction-limited resolution with large aperture transducers [18]. Themethod and apparatus described above have been tested in relation to ahomogeneous medium, with the speed of sound constant along thepropagation path. However, since the speed of sound is a parameter whichmay be optimised, the method described can be adapted to apply tonon-homogeneous media in which the speed of sound varies in space. Inthis case, for example, the medium could be modelled by piecewisecontinuous layers. The optimization method could be applied in arecursive manner, dividing FoV into appropriate sub areas with differentspeeds of sound. More accurate speed of sound estimation may allow forimproved beamforming and allow for higher order phase aberrationcorrection. Furthermore, speed of sound maps are of great interest intissue characterization [19], [20].

To successfully improve the PSF, the multitransducer method describedabove requires coherent alignment of the backscattered echoes frommultiple transmit and receive positions. This requirement is achieved bya precise knowledge of all transducer positions, which in practice isnot possible to achieve by manual measurements or using electromagneticor optical trackers [21]. The method described above allows for preciseand robust transducer location based upon spatial coherence ofbackscattered echoes coming from the same scatter and being received bythe same transducer. The precise location of the transducers requiredfor coherent image creation is calculated by optimizing spatialcoherence. The use of gradient-descent methods requires an initialestimate of the parameters close enough to the global maximum of thecost function. The distance between maxima, which corresponds to thepulse length, dictates this tolerance. For the experimentalconfiguration described above, this is approximately 1.5•s (equivalentto 2.19 mm). This tolerance value can be achieved by imagingregistration [14]. In practice, in a free-hand situation, and assumingthat at some initial instant the registration is accurate, the initialguess can be ensured if the transducers move relatively little in thetime between two transmissions. The method has been validated in afree-hand demonstration.

It will be appreciated that the experimental set up and associatedmethod described above method is limited in that it assumes alltransducers are located on the same plane, i.e. they share the sameimaging plane. An alignment procedure before imaging acquisition hasbeen performed to obtain the images shown in the Figures. The use of a3-D matrix array allows those limitations to be overcome and can be usedto build up higher-resolution volumes than current ultrasound transduceraperture sizes allow. It will also be appreciated that for convergenceof the optimization algorithm described to a unique solution, N pointscatterers, (same as number of transducers), may be needed in the commonFoV. In reality, a plurality of notable scatterers within a medium arelikely, so the limitation is not significant. Whilst the method has beenvalidated for point scatterers, different scatterers may require adifferent approach.

Different transmit and receive paths experience unique clutter effects[22], generating spatially incoherent noise and PSF distortions that canform the basis for further work.

In conventional PW imaging, frame rate is limited by travel andattenuation times, which depend on the speed of sound and theattenuation coefficient. For the experimental setup described above, theminimum time between 2 isonifications is around 94 •s. Hence the maximumframe rate is limited to 10.7 kHz, which is reduced when differentcompounding angles are used. In the case of a multi-transducer method,the frame rate is reduced by the number of transducers as F_(max)/N.

FIG. 11 shows a set of individual sub-images forming a final “multicoherent” image. These were obtained by individually beamforming the 4RF datasets acquired from one complete sequence, i.e. transmitting a PWat 0° with probe T1 and simultaneously receiving with both probes(T₁R₁,T₁R₂) and repeating the transmission with probe T₂ (T₂R₁,T₂R₂).The optimum parameters used to reconstruct the images are •₂=53.05°;O₂=[41.10, 25.00] mm, c=1437:3 m/s. Lines indicate the field of view oftransducer T₁ (upright) and T₂ (slanted).

FIG. 12 shows experimental images of a contrast phantom obtained bydifferent methods. FIG. 12(a) shows coherent plane wave compounding 41PW with transducer T₁;

FIG. 12(b) shows coherent plane wave compounding 41 PW with transducerT₂; FIG. 12(c) shows coherent multi transducer method with transmissionof a single PW at 0° from each transducer; FIG. 12(d) shows coherentmulti transducer method with additional compounding and each transduceremitting 41 PW. The optimum parameters used to reconstruct themulti-coherent images are •₂=53:05°; O₂=[41.10; 25.00] mm, c=1437:3 m/s.Lines indicate the field of view of transducer T₁ (upright) and T₂(slanted).

The results obtained from the anechoic lesion phantom are presented inFIGS. 11 and 12, where the field of view (FoV) of each transducer isindicated by upright and slanted lines (T₁ and T₂ respectively). FIG. 11shows the individual sub-images that form the final multi coherent imageand that are obtained through beamforming the 4 RF datasets acquired ina single cycle of the imaging process, i.e. transmitting a PW at 0° withprobe T₁ and simultaneously receiving with both probes (T₁R₁,T₁R₂) andrepeating the transmission with probe T₂ (T₂R₁,T₂R₂). Reconstruction ofthese sub-images is possible after finding, through optimization,relative positions of the probes. A direct result of the combination ofthese 4 sub images is the extended FoV of the multi coherent image. FIG.12(c) shows a multi coherent image obtained by coherently compounding 4sub-images. It can be seen that, as predicted by a k-spacerepresentation, any overlapping regions in the sub-images willcontribute to improved resolution in the final multi coherent imagebecause of the effective enlarged aperture created.

Images acquired using coherent PW compounding with a single transducer(T₁R₁ and T₂R₂, compounding 41 PW angles) and coherently compounding theRF data acquired by both transducers (using equation (6)) transmittingeach one a single PW at 0° and transmitting each one 41 PW are comparedin FIG. 12.

TABLE II IMAGING PERFORMANCE FOR THE DIFFERENT METHODS ASSESSED USINGTHE CONTRAST PHANTOM. Lateral Frame resolution Contrast CNR rate [mm][dB] [-] [Hz] Single T1R1 2.633 −6.708 0.702 10700 (1 PW at 0°) SingleT1R1 1.555 −8.260 0.795 260 Compounding (41 PW, sector 20°) MultiCoherent 0.713 −7.251 0.721 5350 (1 PW at 0°) Multi Coherent 0.693−8.608 0.793 130 Compounding (41 PW per array, sector 20°)

Table II above shows the corresponding imaging metrics in terms oflateral resolution, contrast, CNR and frame rate. To reconstruct thecoherent multi-transducer images, the initial estimate of parameters waschosen as described above and 3 strong scatterers generated by nylonwires were used in the optimization. It can be seen that, in general,the multi coherent image has better defined edges, making the bordereasier to delineate than in an image obtained by a single transducer.The reconstructed images of the wire targets are clearly improved, thespeckle size is reduced and the anechoic region is easily identifiablefrom the phantom background. Resolution significantly improved in thecoherent multi-transducer method without frame rate sacrifice and atsmall expense of contrast. For single transducer, with coherentcompounding, the lateral resolution, measured at the first targetposition is, 1.555 mm (measured at a frame rate of 260 Hz). Usingmulti-probe image (without additional compounding) the resolutionimproved to 0.713 mm (with an improved frame rate of 5350 Hz). In thesingle transducer case, a lesion is visible with a contrast of −8.26 dBand a CNR of 0.795, while both metrics are slightly reduced in themultitransducer coherent image (without additional compounding) to−7.251 dB and 0.721, respectively. Using compounding with 41 PW overeach probe these improve to −8.608 dB and 0.793. These results suggestthat target detectability is a function of both resolution and contrast.

The dependence of the imaging depth on the angle between both probes hasalso been investigated. FIG. 13 shows a spatial representation of theFoV of two linear arrays and the depth of the common FoV, measured atthe intersection of the centre of both individual fields of view. Thedepth of common FoV as function of the angle between both probes whentransmitting plane waves at 0° is described. It can be seen from FIG. 13that imaging depth increases at larger angle between the probes.

Described arrangements introduce a coherent multi-transducer ultrasoundsystem that significantly outperforms single transducer arrangementsthrough coherent combination of signals acquired by differentsynchronized transducers that have a shared FoV. Although theexperiments described were performed as a demonstration in 2-D usinglinear arrays, the framework proposed encompasses the 3rd spatialdimension. The use of matrix arrays capable of volumetric acquisitionsmay be used for a true 3-D demonstration. Since the multicoherent imageis formed by 4 RF datasets that are acquired in two consecutivetransmissions, it will be appreciated that tissue and/or probe motion donot break the coherence between consecutive acquisitions. To ensure thisis the case, high frame rate acquisition is useful. Whilst describedarrangements use plane waves, different transmit beam profiles such asdiverging waves may increase the overlapped FoV, extending the finalhigh-resolution image. Indeed, there is a complex interplay between FoVand resolution gain as probes are moved relative to one another.

In the method presented overlap of insonated regions allows relativeprobe positions to be determined. Any overlap in either transmit orreceive sensitivity fields contributes to improved resolution because ofthe enlarged aperture of the combination of transducers. The final imageachieves an extended FoV, but the resolution will only improve inregions of overlapping fields. This is best towards the centre whereoverlap includes transmission and reception for both individual probes.There is also an improvement (albeit lesser) in regions where theoverlap is only on transmit or receive fields (see FIGS. 11 and 12).Thus, there are net benefits, but of different kinds, in differentlocations. In a similar way, this also will determine the imaging depthachieved by described methods. Whilst the relative position of theindividual transducers and the angles of the transmitted plane wavesdetermines depth of common FoV (see FIG. 12), an improvement of imagingsensitivity in deep regions is expected since the effective receiveaperture is larger than in a single probe system.

Improvements in resolution are primarily determined by an effectiveextended aperture rather than compounding PW at different angles.Results show that in the coherent multi-transducer method there is atrade-off of between resolution and contrast [18]. While a large gapbetween the probes will result in an extended aperture which improvesresolution, the contrast may be compromised due to the effects ofsidelobes associated with creation of a discontinuous aperture. Furthercoherent compounding can be used to improve the contrast by reducingsidelobes. FIG. 12 illustrates that target detectability is determinedby both resolution and contrast [29]. The differences between k-spacerepresentations for the single and the coherent multi-transducer methodsfurther explain the differences in imaging performance; the moreextended the k-space representation, the higher the resolution [30]. Therelative amplitudes of the spatial frequencies present, i.e. thetopography of k-space, determine the texture of imaged targets.Weighting the individual data from the different transducers can reshapethe k-space, accentuating certain spatial frequencies and so canpotentially create a more conventional response for the system.Moreover, the presence of uniformly spaced unfilled areas in a system'sk-space response may indicate the presence of grating lobes in thesystem's spatial impulse response [28]. A sparse array may create gapsin the k-space response. Only with minimal separation betweentransducers the k-space magnitude response will become smooth andcontinuous over an extended region. This suggests that there is aninterplay between the relative spatial positioning of the individualtransducers and the angles of the transmitted plane waves; where eitherone or both of these can determine the resolution and contrastachievable in the final image [18].

Relative position data can be used to decide what range of PW angles touse and to change these in real time to adaptively change systemperformance. In real life applications, resolution and contrast will beinfluenced by a complex combination of probe separation and angle,aperture width, fired PW angle and imaging depth. It will be appreciatedthat different factors may determine the image performance of thesystem. Image enhancements related to increasing aperture size are welldescribed [12]. Nevertheless, in clinical practice the aperture islimited because extending it often implies increasing system cost andcomplexity. Described implementations use conventional equipment andimage-based calibration to extend the effective aperture size whileincreasing the received amount of RF data (data×N).

Estimated time for “first” initialization of a system in accordance withdescribed arrangements is less than 1 minute, which is comparable toother calibration methods [31], [32]. Once the algorithm has beencorrectly initialized, the subsequent running times for the optimizationcan be significantly decreased. For example, in the free-handexperiment, where each optimization was initialized with the output fromthe previous acquisition, the optimization was up to 4 times faster thanthe first one.

Regarding to the amount of data, similar to 3-D and 4-D ultrafastimaging where the data is significantly large [33], in the proposedmulti-transducer method computation may be a bottleneck for real timeimaging. Graphical processing unit (GPU)-based platforms and high-speedbuses are key to future implementation of these new imaging modes [34].

In addition to the system complexity, large-aperture arrays representergonomic operator problems and have limited flexibility to adapt todifferent applications. In described arrangements, an extended apertureis the result of adding multiple freely placed transducers together,which allows more flexibility. Small arrays are easy to couple to theskin and adapt to the body shape. Whilst use of multiple probes mayincrease the operational difficulty for an individual performing thescan, it is possible to manipulate multiple probes using a single,potentially adjustable, multiprobe holder that would allow the operatorto hold multiple probes with only one hand while keeping directed to thesame region of interest. Such a probe holder has been demonstrated as apotential device for incoherent combination of multiple images forextended FoV imaging [4].

Approaches and arrangements described may provide a different strategyin ultrasound according to which large assemblies of individual arraysmay be operated coherently together. To successfully improve the PSF,multitransducer methods according to arrangements require coherentalignment of backscattered echoes from multiple transmit and receivepositions. This can be achieved through precise knowledge of alltransducer positions, which in practice is not achievable by manualmeasurements or using electromagnetic or optical trackers [35].Approaches described provide methods for precise and robust transducerlocation by maximizing coherence of backscattered echoes arising fromthe same point scatterer and received by the same transducer usingsequential transmissions from each of transducer of a system.

Equivalent to applications providing free-hand tracked ultrasound forimage guide applications [31], [32], spatial calibration helps toguarantee performance of described multi-coherent ultrasound methods. Itwill be appreciated that use of gradient-descent methods requires aninitial estimate of parameters close enough to a global maximum of acost function, including the position of calibration targets. Thedistance between maxima, which depends on NCC and corresponds to thepulse length, dictates this tolerance. This is approximately 1.5•s(equivalent to 2.19 mm) for the experimental configuration describedabove. This tolerance value can be realistically achieved through imageregistration [27]. In practice, in a free-hand situation, and assumingthat at some initial instant the registration is accurate, this initialguess can be ensured if the transducers move relatively little in thetime between two transmissions and share a common FoV. In PW imaging,the frame rate is only limited by the round-trip travel time, whichdepends on the speed of sound and the depth. For the experimental setupdescribed, the minimum time between two insonifications is around 94•s.Hence the maximum frame rate is limited to F_(max)=10:7 kHz, which inthe case of the described multi transducer coherent method, is reducedby the number of probes as F_(max)/N. To guarantee free-hand performanceof the described implementation of a multi transducer method, perfectcoherent summation must be achieved over consecutive transmissions ofthe N transducers of the system. However, when the object underinsonification moves between transmit events, this condition is nolonger achieved. In other words, the free-hand performance is limited bythe maximum velocity at which the probes move. Considering thatcoherence breaks for a velocity at which the observed displacement islarger than half a pulse wavelength per frame [26], the maximum velocityof the probes is V_(max)=•F_(max)/2N, which in the example shown here is1.33 m/s. This speed far exceeds the typical operator hand movements ina regular scanning session and hence, the coherent summation over twoconsecutive transmission is achieved. The method has been validated in afree-hand demonstration.

Wavefront aberration caused by inhomogeneous medium can significantlylimit the quality of medical ultrasound images and is the major barrierto achieve diffraction-limited resolution with large aperturetransducers [36]. The technique described in this work has been testedin a scattering medium, with the assumption of a constant speed of soundalong the propagation path. However, since the speed of sound is aparameter in the optimization, the technique could be adapted fornonhomogeneous media where the speed of sound varies in space [18]. Inthis case, the medium could be modelled through piecewise continuouslayers. The optimization method could be applied in a recursive way,dividing the FoV in sub areas with different speeds of sound. Moreaccurate speed of sound estimation would improve beamforming and allowhigher order phase aberration correction. It will be appreciated that“speed of sound” maps would be of great interest in tissuecharacterization [37], [38].

In addition, the use of multiple transducers allows multipleinterrogations from different angles, which might give insight into theaberration problem and help to test new algorithms to remove theclutter.

The approach presented here has been formulated and validated fordetectable and isolated point scatterers within the shared imagingregion, which in practice may not be always possible. Whilst the theoryhas been presented in relation to point-like scatterers, approaches relyon a measure of coherence which may well be more tolerant, as indicatedin the contrast phantom demonstrated in FIG. 12. This suggests that themethod may work when there are identifiable prominent local features,and the concept of maximizing coherence of data received by eachreceiver array when insonated by different transmitters could allowwider usage. Indeed, an optimization based on spatial coherence might bemore robust in the case where point targets are not available, due tothe expected decorrelation of speckle with receiver location [39]-[41].

This may also lead to improvements in computational efficiency. Measuresof spatial coherence have been used previously in applications such asphase aberration correction [42], flow measurements [43], andbeamforming [44]. On the other hand, isolated point scatterers can beartificially generated by other techniques, for instance by inclusion ofmicrobubble contrast agents [45].

Ultrasound super-resolution imaging recognises that spatially isolatedindividual bubbles can be considered as point scatterers in the acousticfield [46] and accurately localized [47]. The feasibility of thecoherent multi-transducer method in complex media, including a newapproach mainly based on spatial coherence [20], [40] and the potentialuse of microbubbles.

Arrangements described may provide a new coherent multi-transducerultrasound imaging system and a robust method to accurately localize themultiple transducers.

The subwavelength localization accuracy required to merge informationfrom multiple probes is achieved by optimizing the coherence function ofthe backscattered echoes coming from the same point scatterer insonatedby sequentially all transducers and received by the same one, withoutthe use of an external tracking device.

The theory described has application with a multiplicity of 2-D arraysplaced in 3-D and the method was experimentally validated in a 2-Dframework using a pair of linear array and ultrasound phantoms. Theimprovements in imaging quality have been shown. Overall the performanceof the multi-transducer approach is better than PW imaging with onesingle linear array. Results suggest that the coherent multitransducerimaging has the potential to improve ultrasound image quality in a widerange of scenarios.

As described above, a coherent multi-transducer ultrasound imagingsystem (CMTUS) enables an extended effective aperture (super-aperture)through coherent combination of multiple transducers. As describedabove, an improved quality image can be obtained by coherently combiningthe radio frequency (RF) data acquired by multiple synchronizedtransducers that take turns to transmit plane waves (PW) into a commonFoV). In such a coherent multi-transducer ultrasound (CMTUS) method,optimal beamforming parameters, which include the transducer locationsand an average speed of sound in a medium under study, can be deduced bymaximizing coherence of received RF data by cross-correlationtechniques. As a result, a discontinuous large effective aperture (superaperture) is created, significantly improving imaging resolution. Whilethe use of multiple arrays to create a large aperture instead of using asingle big array may be more flexible for different situations such astypical intercostal imaging applications where the acoustic windows arenarrow, the discontinuities dictated by the spatial separation betweenthe multiple transducers may determine the global performance of theCMTUS method. It will be appreciated that as a consequence of thediscontinuous aperture there is a trade-off between resolution andcontrast.

Arrangements recognise that since average speed of sound in a mediumunder study is optimized by the CMTUS method, an improvement in the beamformation with some higher order phase aberration correction isexpected.

Inhomogeneous Media

A k-Wave Matlab toolbox was used to simulate the non-linear wavepropagation through an inhomogeneous medium (Treeby and Cox, 2010;Treeby et al., 2012). A CMTUS system formed by two identical lineararrays, similar to the ones experimentally available, was simulated asfollows:

Each of the arrays had a central frequency of 3 MHz and 144 activeelements in both transmit and receive, with element pitch of 240•m andkerf of 40•m. For plane waves the modelled transducer had an axial focusof infinity with all 144 elements firing simultaneously. The apodisationacross the transducer was modelled by applying a Hanning filter acrossthe transducer width. Table IV summarizes the simulation parameters thatdefine each of the linear arrays.

TABLE IV Parameter Value Number of elements 144 Pitch 240 μm Kerf  40 μmCentral frequency   3 MHz Transmit pulse cycles 3 Sampling frequency30.8 MHz (downsampled)

A simulation was performed for each transmit event, i.e. each plane waveat a certain angle. In total 7 transmit simulations per linear arraywere performed to produce a plane wave data set, which covers a totalsector angle of 30° (from −15° to 15°, 5° step). In the case of CMTUSthis results in 14 transmit events in total (7 plane waves per array).This plane wave sequence was chosen to match in resolution a focusedsystem with F-number 1.9, decimating the required number of angles by afactor of 6 to optimize the simulation time without affectingresolution. The spatial grid was fixed at 40•m (six grid points perwavelength) with a time step corresponding to a Courant-Friedrichs-Lewy(CFL) condition of 0.05 relative to a propagation speed of 1540 m/s.Received signals were downsampled at 30.8 MHz. Channel noise wasintroduced to the RF simulated data as Gaussian noise with a SNR of 35dB at 50 mm imaging depth.

The ultrasound pulses were propagated through heterogeneous scatteringmedia using tissue maps (speed of sound, density, attenuation andnonlinearity). A medium defined only with the properties of general softtissue was used as control case. To model the scattering propertiesobserved in vivo, sub-resolution scatterers were added to the tissuemaps. A total of 15 scatterers of 40•m diameter, with random spatialposition and amplitude (defined by a 5% difference in speed of sound anddensity from the surrounding medium), were added per resolution cell, inorder to fully develop speckle. Three point-like targets and an anechoiclesion were included in the media to allow the measurement of the basismetrics for comparing the imaging quality for different scenarios. Acircular anechoic lesion of 12 mm diameter located at the centre of theaperture of both arrays (common FoV), was modelled as a region withoutscatterers. The point-like targets were simulated as circles of 0.2 mmdiameter with a 25% difference in speed of sound and density with thesurrounding tissue to generate appreciable reflection. The samerealization of scatterers was superimposed on all maps and through thedifferent simulations to keep the speckle pattern in the CMTUS system,so any changes in the quality imaging metrics are due to changes in theoverlying tissues, the imaging depth and the acoustical field.

The k-Wave Matlab toolbox uses a Fourier co-location method to computespatial derivatives and numerically solve the governing model equations,which requires discretisation of the simulation domain into anorthogonal grid. Consequently, continuously defined acoustic sources andmedia need to be sampled on this computational grid, introducingstaircasing errors when sources do not exactly align with the simulationgrid. To minimize these staircasing errors, the transmit array wasalways aligned to the computational grid, i.e. simulations wereperformed in the local coordinate system of the transmit array. Thisimplies that to simulate a sequence in which the array T2 transmits, thepropagation medium, including the sub-resolution scatterers, wasconverted into the local coordinate system of probe T2 using the sametransformation matrix that defines the relative position of bothtransducers in space. A sample tissue map with the transducers,point-like targets and anechoic lesion locations, represented in bothlocal coordinate systems, is shown in FIG. 14.

FIG. 14 illustrates an example of a speed of sound map of a propagationmedium with a muscle layer of 8 mm thickness and a fat layer of 25 mm.Locations of ultrasound probes, point-like targets and anechoic lesionare shown. FIG. 14 (a) shows the medium expressed in the localcoordinate system of the array T1 and used to simulate the RF dataT1R12, i.e. when the array T1 transmits. FIG. 14 (b) shows the mediumexpressed in the local coordinate system of the array T2 and used tosimulate the RF data T2R12, i.e. when the array T2 transmits. In thisexample, the angle between the probes that defines their position inspace is 60° and the corresponding imaging depth 75 mm.

CMTUS Discontinuous Effective Aperture

It is demonstrated above that the discontinuous effective apertureobtained by CMTUS determines the quality of the resulting image. Toinvestigate the effects of the discontinuous aperture, determined by therelative location of the CMTUS arrays in space, different CMTUS systemswith the arrays located at different spatial locations were modelled.Simulations were performed in the same control medium, where only softtissue material was considered. To modify the relative location of theprobes while keeping the imaging depth (fixed at 75 mm), the anglebetween the arrays was changed. The array T1 was always positioned atthe centre of the x-axis of the simulation grid while the array T2 wasrotated around the centre of the propagation medium. Then, differentcases of CMTUS with two arrays located at different angles, from 30° to75° in steps of 15°, were simulated.

FIG. 15 shows a schematic representation of the probes in space, wherethe different spatial parameters (angle between probes, •, and gap, Gap,in the resulting effective aperture, Ef) are labelled. Note that, atlarger angles, both the effective aperture of the system defined by bothprobes and the gap between them increase. The relationships betweenprobe position, and the resulting effective aperture and gap are shownin FIG. 15.

CMTUS Image Penetration

The image penetration of CMTUS was investigated by changing the localorientation of the arrays and using the same control propagation medium(only soft tissue). For a given effective aperture (fixed gap), eachprobe was rotated around its centre the same angle but in the oppositedirection. In that way, a certain given rotation, for example negativein T1 and positive in T2 will result in a deeper common FoV, and theopposite for the counter-rotation. FIG. 16 shows the imaging depthdependence on the transducer orientation (defined by the position of thecommon FoV of both arrays). Using this scheme, four different imagingdepths were simulated: 57.5 mm, 75 mm, 108 and 132 mm.

FIG. 16 shows a schematic representation of the spatial location of thetwo linear arrays, T1 and T2, and their field of view at differentimaging depths. The imaging depth is obtained steering the linear arraysthe same angle but in opposite directions. Three different cases areshown: (a) 57.5 mm imaging depth; (b) 75 mm imaging depth; and (c) 108imaging depth. The circle indicates the centre of the common field ofview, which defines the imaging depth in CMTUS.

CMTUS Through Aberrating Media

To investigate the effect of aberrating inhomogeneities in the medium,three different kinds of tissue were defined in the propagation media(general soft tissue, fat and muscle). The imaging depth was set to 75mm with a configuration of the arrays in space that defines an effectiveaperture of 104.7 mm with 45.3 mm gap. The acoustic properties assignedto each tissue type were chosen from the literature and are listedbelow:

Tissue Speed of Density Attenuation Nonlinearity type Sound [m/s][kg/m³] [dB/MHz/cm] B/A Soft 1540 1000 0.75 6 tissue Fat 1478 950 0.6310 Muscle 1547 1050 0.15 7.4

A medium defined only with the soft tissue properties was used ascontrol case. Then, clutter effects were analysed by using heterogenousmedia in which two layers with the acoustic properties of muscle and fatwere introduced into the control case medium. In the different studiedcases, the thickness of the muscle layer was set to 8 mm while fatranged from 5 to 35 mm thickness. FIG. 14 shows an example of thepropagation medium with a muscle layer of 8 mm and a fat layer of 25 mm.

In-Vitro Experiments

A sequence similar to the one used in simulations was used to image aphantom. The imaging system consisted of two 256-channel UltrasoundAdvanced Open Platform (ULA-OP 256) systems (MSD Lab, University ofFlorence, Italy). The systems were synchronized, i.e. with the sametrigger and sampling times in both transmit and receive mode. Each ULAOP256 system was used to drive an ultrasonic linear array made of 144piezoelectric elements with a 6 dB bandwidth ranging from 2 MHz to 7.5MHz (imaging transducer LA332, Esaote, Firenze, Italy). The two probeswere mounted on xyz translation and rotation stage (Thorlabs, USA) andwere carefully aligned in the same elevational plane (y=0). For eachprobe in an alternating sequence, i.e. only one probe transmits at eachtime while both probes receive, 7 PW, covering a total sector angle of300 (from −15° to 15°, 5° step), were transmitted at 3 MHz and pulserepetition frequency (PRF) of 1 kHz. RF data backscattered up to 135 mmdeep were acquired at a sampling frequency of 19.5 MHz. No apodizationwas applied either on transmission or reception. A subset of thesimulated results was experimentally validated in-vitro. A phantomcustom made with three point-like targets and ananaechoic region, wasimaged with the imaging system and pulse sequences described below. Theaveraged speed of sound of the phantom was 1450 m/s. The phantom wasimmersed in a water tank to guarantee good acoustic coupling. To induceaberration, a layer of paraffin wax of 20 mm thickness was placedbetween the probes and the phantom. The measured speed of sound ofparaffin wax was 1300 m/s.

The control experiment was performed first without the paraffin waxsample present. After the control scan, the paraffin wax sample waspositioned over the phantom without movement of the phantom or tank.Then, the target was scanned as before. The paraffin wax sample waspositioned to sit immediately over the phantom, coupled to thetransducers by water. A final control scan was performed to verifyregistration of the phantom, tank and transducers, after the paraffinwax sample was scanned and removed.

Data Processing

The RF data, both simulated and experimentally acquired, were processedin different combinations to study image quality. For a single probesystem, beamforming of RF data was performed using the conventionaldelay-and-sum method for coherent plane wave compounding. Themulti-transducer beamforming was performed as described above.

For each simulated case, the optimum beamforming parameters, calculatedby maximizing the cross-correlation of backscattered signals from commontargets acquired by individual receive elements as described above wereused to generate CMTUS images. For the simulated RF data, where theactual position of the arrays in space is known, an additional image,noted as 2-probes, was beam-formed by assuming a speed of sound of 1540m/s and using the spatial location of the array elements. Note that, inthe experimental case this is not possible because the actual positionof the arrays in space is not accurately known a priori. Finally, thedata corresponding to the sequence when the array T1 transmits andreceives, i.e. T₁R₁, and noted here as 1-probe, was used as a base linefor array performance, providing a point of comparison to the currentcoherent plane wave compounding method in both simulated andexperimental scenarios. Note that, for all the cases except CMTUS, anassumed value of the speed of sound was used to beamform the data (1540m/s for simulated data and 1450 m/s for experimental data).

In order to achieve a comparison between imaging modalities as fair aspossible in terms of transmitted energy, the CMTUS and the 2-probesimages are obtained by compounding only 6 different PW, while the 1probe system images are generated compounding the total number of thetransmit plane waves, i.e. 7 PW from −15° to 15°, in 5° step. In thatvein, the CMTUS and 2-probes images are the results of compounding theRF data when the array T1 transmits PW at zero and positive angles (0°,5°, 10°) and the array T2 transmits PW at zero and negative angles (0°,−5°, −10°). An even number of transmissions was set because the CMTUSoptimization is based on a pair of transmissions, one per array. Inaddition, firing at opposite angles with the 2 arrays guarantees theCMTUS performance since an overlap of the isonated regions is mandatoryto determine the relative probe-to-probe position.

For each resulting image, lateral resolution (LR), contrast andcontrast-to-noise ratio 273 (CNR) were measured to quantify the impactof both the aperture size and the clutter. LR was calculated from thepoint-spread-function (PSF) of the middle point-like target. Anaxial-lateral plane for 2-D PSF analysis was chosen by finding thelocation of the peak value in the elevation dimension from theenvelope-detected data. Lateral and axial PSF profiles were taken fromthe centre of the point target and aligned with the principal resolutiondirections. LR was then assessed by measuring the width of the PSF atthe −6 dB level. The contrast and CNR were measured from theenvelope-detected images. Contrast and CNR were calculated as:

Contrast=20 log₁₀(μ_(i)/μ_(o))

CNR=|μ _(i)−μ_(o)|/√{square root over (μ_(i) ²+μ_(o) ².)}

Where μ_(i) and μ_(o) are the means of the signal inside and outside ofthe region, respectively. All image metrics were computed beforelog-compress transformation was applied.

Results

A. Simulation Results

Control Case: Conventional Aperture Imaging

The conventional aperture image, corresponding to the sequence when thearray T1 transmits and receives, i.e. T1R1 (1-probe), provides the baseline for imaging quality through the different scenarios.

FIG. 17 illustrates the resulting image at 75 mm depth and without anyaberrating layer in the propagation medium. A speed of sound of 1540 m/swas used to reconstruct these images. The point target (FIG. 17(b)) hasa lateral resolution of 1.78 mm and the lesion (FIG. 17(c)) is visiblewith a contrast of −16.78 dB and CNR of 0.846. Note that, while thelesion is easily identified from the background, it is difficult todelineate its edges.

CMTUS Discontinuous Effective Aperture

FIG. 18 shows a simulated PSF and lesion images from the samenon-aberrating medium and for increasing effective aperture and gap ofthe CMTUS system. It can be seen that, the PSF depends on the size ofthe effective aperture and the gap between the probes. As expected, thecentral lobe of the PSF reduces in width with increase in size of theeffective aperture. However, while at extended apertures the width ofthe main lobe decreases, the amplitude of the side lobes increases withthe corresponding gap in the aperture, affecting contrast as can be seenin the lesion images. The effects of the side lobes in the image qualitycan be seen in FIG. 18, where an effective aperture with a gap of 64.1mm significantly raises the amplitude of the side lobes close to themain lobe's one and affects the lesion image.

FIG. 19 compares corresponding computed image quality metrics (LR,contrast and CNR) as function of the obtained effective aperture.Results show that both the main lobe of the PSF and the lateralresolution decrease with larger effective aperture size. Since anincreasing effective aperture represents also a larger gap between theprobes, contrast and resolution follow opposite trends. In general,comparing with the 1-probe system, CMTUS produces the best lateralresolution in all the cases but shows degradation in contrast at theparticular imaging depth of 75 mm. At the maximum effective aperturesimulated, resolution is the best with 0.34 mm, while the contrast andCNR drop to a minimum of −15.51 dB and 0.82, respectively. FIG. 19 showsthe lateral point spread functions extracted from FIG. 18 at the depthof peak point intensity and in the principal direction. Correspondingcomputed quality metrics as function of the effective aperture size inCMTUS: Lateral resolution (LR) measured at −6 dB from the lateral pointsspread function, contrast and contrast-to-noise-ratio (CNR) measured onFIG. 18.

CMTUS Image Penetration

FIG. 20 compares CMTUS images with the 1-probe system at two differentimaging depths (100 mm and 155 mm). Image degradation with depth isclearly observed in all the cases. However at larger depths the 1-probeshows a greater level of degradation. At the maximum imaging depth shown(155 mm), the point targets and the lesion can still be identified inthe CMTUS image while in the 1-probe image is not obvious.

FIG. 21 summarises computed image metrics as a function of imagingdepth. As expected, in both systems, all image metrics worsen at largerimaging depths. Nevertheless, results show that their dependence on theimaging depth is different between the 1-probe and the CMTUS cases. Theslope of the curve LR-depth is significantly higher in the 1-probesystem than in the CMTUS method, which suggests that loss in resolutionwith imaging depth is faster at smaller apertures. While at reducedimaging depths (<100 mm) contrast and CNR seem to be affected in asimilar way in both systems, the loss in contrast metrics are lessaccentuated in the CMTUS system at depths larger than 100 mm, whereCMTUS method overcomes the performance of the 1-probe system not only interms of resolution but also in contrast. The extended effectiveaperture created by CMTUS consequently increases the sensitivity of theimaging system, particularly at large imaging depths.

CMTUS Through Aberrating Media

FIG. 22 is a comparison of simulated images acquired by a conventionalaperture 1-probe (a-d), 2-probes (e-h) and CMTUS method (i-l) throughaberrating layers of increasing thickness (thickness of fat layerincreases from 0 mm, 10 mm, 25 mm to 35 mm). 1-probe images using 7 PWtransmissions; 2-probes and CMTUS images using 6 PW transmissions.

FIG. 22 shows the simulated images for the control case (propagationmedium only with soft tissue) and for imaging through aberrating layersof different thickness. The different methods, i.e. i-probe, 2-probesand CMTUS are compared. It can be seen that, in the presence ofaberration, the PSF and contrast of the 2-probes image signicantlydegrade when comparing with the control case. This effect is clearlyseen in the point targets imaged through a fat layer of 35 mm thickness,where results show that if aberration is not corrected, extendedapertures do not show benefits in terms of resolution. Indeed, in thepresence of aberration, it is not possible to coherently reconstruct theimage using the two separate transducers (2-probes system case).

FIG. 23 shows simulated delayed RF data for a medium with a fat layer of35 mm thickness and backscattered from a point-like target, obtained bycoherently adding the 4 delayed backscattered echoes from the samepoint-like target (T1R1; T1R2; T2R1; T2R2) and different beamformingparameters: FIG. 23(a) 2-probes; FIG. 23(b) CMTUS.

FIG. 23 shows an example of the delayed echos from the point-like targetfor the 2-probes and CMTUS cases, corresponding to a propagation mediumwith a fat layer of 35 mm thickness. These flat backscattered echoes areobtained by coherently adding the 4 delayed backscattered echoes fromthe same point-like target (T1R1; T1R2; T2R1; T2R2) and thecorresponding beamforming parameters. It is worth pointing out that inthe 2-probes case, the different echoes do not properly align, creatinginterference when coherently adding them together. However, afteroptimizing the beamforming parameters in the CMTUS, all echos alignbetter and can be coherently added together, minimizing the aberratingconsequences. Similar effects are seen in the anechoic lesion. Whiledifferences in the background speckle pattern are observed between thedifferent imaging methods, a higher loss of contrast due to aberrationcan be appreciated only in the 2-probes images. Nevertheless, nosignificant changes in imaging quality because of aberration areappreciated in either the 1-probe or CMTUS systems. Although bothsystems are able to image through aberrating layers, they show cleardifferences. The CMTUS shows more detailed images than the 1-probesystem. The speckle size is reduced and the different tissue layers areonly visible in the CMTUS images.

FIG. 24 is a comparison of computed quality metrics across differentimaging methods. FIG. 24 shows computed quality metrics, lateralresolution (LR), contrast and contrast-to-noise-ratio (CNR), as functionof the clutter thickness (fat layer). Three different methods arecompared: 1-probe coherent plane wave compound using 7 PW transmissions,2-probes using 6 PW transmissions and CMTUS using 6 PW transmissions.Imaging metrics as function of fat layer thickness are shown. Asexpected, in the absence of aberration, resolution improves withincreasing aperture size. In this case, the worst lateral resolutioncorresponds to 367 the 1-probe system with 1.78 mm, which is the onewith smallest aperture size, while the 368 2-probes and CMTUS images aresimilar with 0.40 mm. The trends show that if aberration is notcorrected, there are no significant improvements in the imaging metricsrelated to the aperture size for thicker thickness of fat layers. Atclutter thickness larger than 10 mm, image quality of the system formedby 2 transducers without aberration correction (2-probes) issignificantly degraded, while CMTUS imaging metrics are not affected byaberration errors, following the same trend as a conventional aperture(1-probe) and providing a constant value of resolution over clutterthickness without any significant loss of contrast. At the thickest fatlayer simulated, resolution is 1.7 mm and 0.35 mm for the 1-probe andCTMUS images, respectively, while in the case of 2-probes images is nolonger possible to reconstruct the point-target to measure resolution.Contrast and CNR also show a similar significant loss for the 2-probesimage that presents a contrast of −10.84 dB and CNR of 0.69, while thosevalues are significantly better for the 1-probe (−18.44 dB contrast and0.87 CNR) and CMTUS (−17.41 dB contrast and 0.86 CNR) images.

Experimental Results

Coherent plane wave imaging with a conventional aperture imaging (usinga single probe) provides the reference for image quality with andwithout the paraffin wax layer. To reconstruct these images thereference speed of sound in water of 1496 m/s was used and 7 PW werecompounded.

FIG. 25 shows experimental images of a control (a,c) and the paraffincases (b,d). Two different methods are compared: 1-probe coherent planewave compound using 7 PW transmissions (a,b) and CMTUS using 6 PWtransmissions (c,d). FIG. 25 shows a comparison of the phantom imagesacquired with 1-probe and CMTUS in the control case and through aparaffin wax sample. The CMTUS images were reconstructed using theoptimum beamfoming parameters, which include the average speed of soundand compounding 6 PW. All images are shown in the same dynamic range of−60 dB. In both cases, 1-probe and CMTUS images, little variation isobserved between the control and the paraffin images, which agree withthe simulation results. The value of the optimum beamforming parametersused to reconstruct the CMTUS images is {c=1488.5 m/s; •₂=30.04°;r₂=[46.60, 12.33] mm} for the control case and {c=1482.6 m/s, •₂=30:000;r₂=[46.70, 12:37] mm} for the paraffin. There are slight changes in allthe values and a drop in the average speed of sound which agrees withthe lower speed of propagation of sound of the paraffin wax.

FIG. 26 shows a comparison of computed quality metrics, lateralresolution (LR), contrast and contrast-to-noise-ratio (CNR),experimentally measured for two different acquisition techniques. Twodifferent methods are compared: 1-probe coherent plane wave compoundusing 7 PW transmissions and CMTUS using 6 PW transmissions. FIG. 26summarizes the computed image metrics for both the control and theparaffin cases. Little variation was observed in all the imagingmetrics. Although minimum image degradation by aberrating layers wasobserved in the CMTUS, the overall image quality improved compared withthe conventional single aperture and the observed image degradationfollows the same trend.

FIG. 27 compares experimental point target images. The first pointtarget located at 85 mm depth was described using its lateral PSF withand without the paraffin wax layer. No significant effects due to theaberration are observed in the PSF in any of the cases. The PSF shape issimilar with and without the paraffin wax layer and agree with the oneobserved in simulations. In general, the CMTUS method leads to a PSFwith significant narrower main lobe but also with side lobes of biggeramplitude than the 1-probe conventional imaging system.

FIG. 27 shows experimental point target images. Column (a) correspondsto the control and column (b) to the paraffin. First row corresponds to1-probe system and middle row to CMTUS. Bottom row shows thecorresponding lateral point spread functions for the two casesdisplayed: 1-probe system (dashed line) and CMTUS (solid line). 1-probeimages using 7 PW transmissions. CMTUS images using 6 PW transmissions.

FIG. 28 shows the coherent summation of the delayed echos from thepoint-like target before and after optimization. The effects of theparaffin layer are clearly seen. When the beamforming parameters,including the averaged speed of sound, are optimized by the CMTUSmethods, all echos align better, minimizing the aberrating paraffineffects. FIG. 28 shows experimental delayed RF data acquired from thephantom with the paraffin wax sample. CMTUS flat backscattered echo froma point-like target, obtained by coherently adding the 4 delayedbackscattered echoes from the same point-like target (T1R1; T1R2; T2R1;T2R2) using different beamforming parameters: (a) initial guess values;(b) optimum values.

DISCUSSION

The implications for imaging using the CMTUS method with two lineararrays have been investigated here with simulations and experiments. Theanalysis shows that the performance of the CMTUS depends on the relativelocation of the arrays, the CMTUS sensitivity increases with the imagingdepth and the resulting extended aperture preserves in the presence ofaberration. These findings show that, if the separation betweentransducers is limited, the extended effective aperture created by CMTUSconfers benefits in resolution and contrast that improve image qualityat large imaging depths and even in the presence of acoustic clutterimposed by tissue layers of different speed of sound. Unlike theimprovement achieved in resolution, benefits in contrast are not sosignificant.

Simulation results suggest that, the discontinuous effective aperturemay degrade contrast when the gap in the aperture is bigger than a fewcentimeters. In probe design, there is a requirement of half wavelengthspacing between elements in order to avoid the occurrence of unwantedgrating lobes in the array response. Moreover, previous studiesindicated that, unlike resolution, contrast does not continue toincrease uniformly at larger aperture sizes. Nevertheless, while thecontrast may be degraded by big discontinuities in the aperture, themain lobe resolution continues to improve at larger effective apertures.Since the lesion detectability is a function of both the contrast andresolution overall there are benefits from extended aperture size, evenwhen contrast is limited. A narrow main lobe allows fine sampling ofhigh resolution targets, providing improved visibility of edges ofclinically relevant targets. In addition, when imaging at larger depths,an extended aperture has the potential to improve theattenuation-limited image quality. In those challenging cases at largeimaging depths, CMTUS shows improvements not only in resolution but alsoin contrast.

Results agree with the hypothesis that in the absence of aberration, theaperture size determines resolution. However, previous work suggeststhat despite predicted gains in resolution, there are practicallimitations to the gains made at larger aperture sizes. Inhomogeneitiescaused changes in the side lobes and focal distance, limiting theimprovement in resolution. The resulting degradation is primarilythought to be arrival time variation called phase aberration. The outerelements on a large transducer suffer from severe phase errors due to anaberrating layer of varying thickness, placing limits on the gains to bemade from large arrays.

Findings presented here agree with these previous studies, and in thepresence of aberration clutter, aperture size will be limited inpractice. Nevertheless, the CMTUS method takes into account the averagespeed of sound in the medium and shows promise for extending theeffective aperture beyond this practical limit imposed by the clutter.More accurate speed of sound estimation would improve beamforming andallow higher order phase aberration correction. However other challengesimposed by aberration still remain.

Both phase aberration and reverberation can be primary contributors todegraded image quality. While phase aberration effects are caused byvariations in sound speed due to tissue inhomogeneity, reverberation iscaused by multiple reflections within inhomogeneous medium, generatingclutter that distorts the appearance of the wavefronts from the regionof interest. For fundamental imaging, reverberations have been shown tobe a significant cause of image quality degradation and are theprincipal reason why harmonic ultrasound imaging is better thanfundamental imaging. It is envisaged that the role of redundancy in thelarge array in averaging multiple realizations of the reverberationsignal may provide a mechanism for clutter reduction.

Whilst some choices made in the design of described experiments may notdirectly translate to clinical practice, it will be appreciated thatthey do not compromise the conclusions drawn from the results set outabove. For example, the available H6J experimental setup drove theelection of the frequency, which is higher than is traditionally used inabdominal imaging (1-2 MHz). In addition, although both the simulatedand experimental phantoms are a simplistic model of real human tissue,they are able to capture the main potential causes that degradeultrasound images, including attenuation, gross sound speed error, phaseaberration, and reverberation clutter.

Although illustrative embodiments of the invention have been disclosedin detail herein, with reference to the accompanying drawings, it isunderstood that the invention is not limited to the precise embodimentand that various changes and modifications can be effected therein byone skilled in the art without departing from the scope of the inventionas defined by the appended claims and their equivalents.

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1. An ultrasound method comprising: providing, from each of two or moreseparate ultrasound transmitters, a signal into a coincident region;receiving, at a receiving array, wavefronts representative of theprovided signal from each of the two or more separate ultrasoundtransmitters after interaction of the provided signal with a mediumlocated within the coincident region; analyzing the received wavefrontsto determine a relative spatial position of each of the two or moreseparate ultrasound transmitters; and based on the determined relativespatial position of each of the two or more separate ultrasoundtransmitters, performing a coherent signal combination of the receivedwavefronts received at the receiving array based on the provided signalfrom each of the two or more separate ultrasound transmitters afterinteraction of the provided signal with the medium located within thecoincident region.
 2. The ultrasound method according to claim 1,wherein analyzing the received wavefronts comprises selecting one ormore parameters defining the determined relative spatial position ofeach of the two or more separate ultrasound transmitters.
 3. Theultrasound method according to claim 2, wherein analyzing the receivedwavefronts comprises using the received wavefronts to make an initialguess at one or more parameters defining the relative spatial positionof each of the two or more separate ultrasound transmitters.
 4. Theultrasound method according to claim 2, wherein said analyzing thereceived wavefronts comprises receiving an indication of one or moreparameters defining the relative spatial position of each of the two ormore separate ultrasound transmitters from one or more orientationsensors associated with each of the two or more separate ultrasoundtransmitters.
 5. The ultrasound method according to claim 2, wherein theone or more parameters comprise a combination of parameters which allowthe relative spatial position of each of the two or more separateultrasound transmitters to be determined.
 6. The ultrasound methodaccording to claim 2, wherein the one or more parameters comprise one ormore of: a location of one or more scatterer located within the mediumlocated within the coincident region; a relative angle between the twoor more separate ultrasound transmitters; a relative distance of the twoor more separate ultrasound transmitters from the receiving array; or aspeed of sound within the medium located within the coincident region.7. The ultrasound method according to claim 2, wherein analyzing thereceived wavefronts comprises increasing correspondence between thereceived wavefronts by refining the one or more parameters defining therelative spatial position of each of the two or more separate ultrasoundtransmitters.
 8. The ultrasound method according to claim 7, whereinsaid correspondence comprises a correlation between the receivedwavefronts.
 9. The ultrasound method according to claim 7, furthercomprising using the refined one or more parameters to select therelative spatial position to be used when performing the coherent signalcombination.
 10. (canceled)
 11. An ultrasound apparatus comprising: twoor more separate ultrasound transmitters positioned to transmit a signalinto a coincident region, a receiving array for receiving a wavefrontrepresentative of a transmitted signal from each of the two or moreseparate ultrasound transmitters after interaction of the transmittedsignal with a medium located within the coincident region; locationprocessing logic to analyze each of the received wavefronts anddetermine a relative spatial position of each of the two or moreseparate ultrasound transmitters; and signal combination logic to usethe determined relative spatial position of each of the two or moreseparate ultrasound transmitters to perform coherent signal combinationof the received wavefronts received at the receiving array from each ofthe two or more separate ultrasound transmitters after interaction ofthe transmitted signal with the medium located within the coincidentregion.
 12. The ultrasound apparatus according to claim 11, wherein thetwo or more separate ultrasound transmitters are located such that theirsignal volumes at least partly overlap within the coincident region. 13.The ultrasound apparatus according to claim 11, wherein the two or moreseparate ultrasound transmitters provide the transmitted signal into thecoincident region substantially concurrently.
 14. The ultrasoundapparatus according to claim 11, wherein the two or more separateultrasound transmitters provide the transmitted signal into thecoincident region consecutively.
 15. The ultrasound apparatus accordingto claim 11, wherein the transmitted signal from each of the two or moreseparate ultrasound transmitters comprises a plane wave.
 16. Theultrasound apparatus according to claim 11, wherein the ultrasoundapparatus further comprises: an additional receiving array to receivethe wavefront representative of the transmitted signal from each of thetwo or more separate ultrasound transmitters after interaction of thetransmitted signal with the medium located within the coincident region;wherein the location processing logic analyzes each of the receivedwavefronts received at the receiving array and the additional receivingarray to determine the relative spatial position of each of the two ormore separate ultrasound transmitters; and wherein the signalcombination logic uses the determined relative spatial position of eachof the two or more separate ultrasound transmitters from the receivingarray and the additional receiving array to perform coherent imagereconstruction of the medium located within the coincident region bycombining the received wavefronts.
 17. The ultrasound apparatusaccording to claim 16, wherein at least one of the two or more separateultrasound transmitters and one or more of the receiving array and theadditional receiving array are co-located to form an ultrasoundtransducer.
 18. A non-transitory computer readable storage mediumstoring instructions thereon that, when executed by at least oneprocessor, cause a computer device to: provide, from each of two or moreseparate ultrasound transmitters, a signal into a coincident region;receive, at a receiving array, wavefronts representative of the providedsignal from each of the two or more separate ultrasound transmittersafter interaction of the provided signal with a medium located withinthe coincident region; analyze the received wavefronts to determine arelative spatial position of each of the two or more separate ultrasoundtransmitters; and based on the determined relative spatial position ofeach of the two or more separate ultrasound transmitters, perform acoherent signal combination of the received wavefronts received at thereceiving array based on the provided signal from each of the two ormore separate ultrasound transmitters after interaction of the providedsignal with the medium located within the coincident region.
 19. Thenon-transitory computer readable storage medium of claim 18, whereinanalyzing the received wavefronts comprises selecting one or moreparameters defining the determined relative spatial position of each ofthe two or more separate ultrasound transmitters.
 20. The non-transitorycomputer readable storage medium of claim 19, wherein the one or moreparameters comprise a combination of parameters which allow the relativespatial position of each of the two or more separate ultrasoundtransmitters to be determined.
 21. The non-transitory computer readablestorage medium of claim 19, wherein the one or more parameters compriseone or more of: a location of one or more scatterer located within themedium located within the coincident region; a relative angle betweenthe two or more separate ultrasound transmitters; a relative distance ofthe two or more separate ultrasound transmitters from the receivingarray; or a speed of sound within the medium located within thecoincident region.